When shaping tubular workpieces from thermoplastic plastics, the procedure is such that the workpiece is placed as a semifinished product in a non-shaped state, in a complex mold, whereupon the entire device is heated in a liquid bath or hot-air furnace and then cooled. The action of heat and subsequent cooling gives the workpiece the shape determined by the mold. A disadvantage of this known method is that the working of the method is associated with high energy consumption. Large amounts of energy are consumed both in heating in the liquid bath and heating in the hot-air furnace. In the bath method, moreover, large amounts of auxiliary substances are consumed, and in the air method long cycle times are always involved. These disadvantageous features also result in high system operating costs, which result in an increased cost for the entire method.